I'm not able to reproduce this here (using NeoBook v5.8.6, IE v11.0.10240.16431 and Windows 10).

It sort of sounds like Windows or your firewall/AV thinks NeoBook isn't allowed to access the Internet. NeoBook might not be stuck, but just waiting for the Internet request to timeout which might take a minute or so.

Disabling AV has no effect.When started, neobook spawns two neobook.exe processes (never noticed this before, is it correct?) When traversing wait chain in task manager it shows that one process waits for another indefinitely (deadlock?)

But then some magic things happened when I tried to attach debugger to neobook.exe process, it told me that will never work under debugger and terminated. After that, all issues have gone.I guess these issues was caused by the fact that multiple versions of neobook (5.6.4/5.7.0/5.8.6 trials) installed and used on the same machine, maybe something went wrong with armadillo protection environment.